Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22577956 | C2 | semidirect |
| 3. #22577766 | C2 | semidirect |
| 4. #22577748 | C2 | semidirect |
| 5. #22577409 | C2 | semidirect |
| 6. #22577408 | C2 | semidirect |
| 7. #22577407 | C2 | semidirect |
| 8. M16×Dic137 | C2 | semidirect |
| 9. #418×C137 | C2 | semidirect |
| 13. #17984087 | C22 | semidirect |
| 17. #17984079 | C22 | semidirect |
| 22. #17984010 | C22 | semidirect |
| 23. #17984009 | C22 | semidirect |
| 24. #17984008 | C22 | semidirect |
| 25. #17983998 | C22 | semidirect |
| 26. C8×Dic137 | C22 | semidirect |
| 30. #102×C137 | C22 | semidirect |
| 111. C137 | #3138 | semidirect |
| 120. #418 | D137 | semidirect |
| 140. #102 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577956 | 2 |
| C2×#17984084 | 2 |
| #22577766 | 2 |
| #22577748 | 2 |
| #22577409 | 2 |
| #22577408 | 2 |
| #22577407 | 2 |
| M16×Dic137 | 2 |
| #418×C137 | 2 |
| #3138 | 137 |